Straight-edge Tangent Line Construction
Two tangent lines PP_1 and PP_2 were constructed using only point P, three arbitrary points R_1, R_2, and R_3, and a straight-edge. The center of the circle, O, was not needed for the construction, but you can use it to check that PP_1 and PP_2 really are tangent to this circle. Try moving P around to see the different tangent lines that result!